The purpose of this phase II study is to determine whether oral interferon-alpha (IFN-a) can decrease enhancing lesions on brain MRI (paraclinical outcome) and IFN-gamma secretion (immunological outcome) in patients with relapsing remitting multiple sclerosis (MS). Patients will be randomized to receive placebo, 10,000 or 30,000 units on alternate days for nine months. If IFN-a shows immunological, MRI paraclinical effects or toxicity in subjects, it will provide dosing information essential to evaluate the drug in future studies as a treatment in MS patients.